Two examples of $varepsilon$-famed manifolds are constructed. It is proved that an $varepsilon$-framed structure on a manifold is not unique. Automorphism groups of r-framed manifolds are studied. Lastly we prove that a connected Lie group G admits a left invariant normal $varepsilon$-framed structure if and only if the Lie algebra of all left invariant vector fields on G is an $varepsilon$-framed Lie algebra.